Altay, BBasar, FMursaleen, M2024-08-042024-08-0420060020-0255https://doi.org/10.1016/j.ins.2005.05.008https://hdl.handle.net/11616/94293In the present paper, we introduce the Euler sequence space e(p)(r) consisting of all sequences whose Euler transforms of order r are in the space e,, of non-absolute type which is the BK-space including the space l(p) and prove that the spaces e(p)(r) and l(p) are linearly isomorphic for 1 <= p <= infinity. Furthermore, we give some inclusion relations concerning the space e(p)(r). Finally, we determine the alpha-, beta- and gamma-duals of the space e(p)(r) for 1 <= p <= infinity and construct the basis for the space e(p)(r), where 1 <= P <= infinity. (c) 2005 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessEuler sequence spaces of non-absolute typeBK-spaceThe alpha-, beta- and gamma-dualsSchauder basisArticle176101450146210.1016/j.ins.2005.05.0082-s2.0-33644690630Q1WOS:000236435000009Q2